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Author Topic: How would gravity behave inside a hollow planet?  (Read 17354 times)

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #25 on: 27/07/2013 15:57:28 »
It is manifestly absurd to say "in my opinion, 1+1 =3": you can't have an opinion about matters of fact.
And it is equally absurd to say what Thibeninn said about gravity because that assertion was proven false centuries ago.
And to continue to say it, after that proof has been pointed out is just silly.
People who don't know calculus can't follow the derivation. But to think that everyone of us who can have all made the exact mistake is hillareously silly.
 

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Re: How would gravity behave inside a hollow planet?
« Reply #26 on: 27/07/2013 17:16:34 »
Thibeinn, you may find these links interesting
Quote
In the same way, one can show that inside the hollow interior of a spherical shell (or any other spherically symmetric hollow mass configuration), there are no gravitational forces at all.
From  http://www.einstein-online.info/spotlights/gravity_of_gravity

Quote
Gravitation Inside A Uniform Hollow Sphere
The gravitational force inside a hollow sphere shell of uniform areal mass density is everywhere equal to zero, and may be proved by the following argument:
from http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/grvtysp.htm

Quote
The net gravitational force on a point mass inside a spherical shell of mass is identically zero!
From http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.html

Quote
Field Inside a Spherical Shell
This turns out to be surprisingly simple!  We imagine the shell to be very thin, with a mass density  kg per square meter of surface. Begin by drawing a two-way cone radiating out from the point P, so that it includes two small areas of the shell on opposite sides: these two areas will exert gravitational attraction on a mass at P in opposite directions.  It turns out that they exactly cancel.
From http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm


« Last Edit: 27/07/2013 17:20:12 by lean bean »
 

Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #27 on: 28/07/2013 01:18:23 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!

See: http://en.wikipedia.org/wiki/Shell_theorem#Converses_and_generalisations
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #28 on: 28/07/2013 02:40:57 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!
I disagree. It's easy to create a hollow shell. Just get a small asterod and make it spherical and then hollow it out. It can be done. It's just not something anybody would want to do because nobody who knows anything about gravity doubts it. One could make a sphere on earth and then measure the field inside and compare it to what the field is like when the shell isn't there. It should be the same. I believe we can make measurements of the gravitational field that accurately
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #29 on: 28/07/2013 05:59:45 »
Iím going to take another shot at this in hopes Thibeinn just isnít seeing what we all know intuitively and from knowing how these things work out in calculations.

Quote from: Thibeinn
Such a statement as, "gravity inside a hollowed out planet is zero", is scientifically unsound.
Do you know what the term ďunsoundĒ means? It means ďnot true.Ē This means that you know of a hollow shell in which the gravitational field was not zero. Otherwise itís theoretical and thereís no reasoning that can lead to such a theoretical prediction.

Newtonís law states that if you have two objects which are small enough to be approximated as point objects and if one of mass m1 and the other has mass m2 then the force on object 1 due to object 2 has the magnitude

F = G m1 m2/r[sup2[/sup]

Where r is the distance between the centers of the objects. This is true regardless of what lies in-between the two objects so long as the gravitational force of what lies in between is taken into account. The direction of the force directed from object 2 to object 1. If there are other bodies whose sizes can be neglected them the principle of superposition applies.

In order to determine the gravitational field inside a hollow shell of mass one calculates the force by considering a large number of small pieces of the shell and let the size of the shell go to zero as the number of pieces goes to infinity and you add up all the contributions. This process is called ďintegrationĒ and is a process invented by Newton for these very kinds of purposes.

Quote from: Thibeinn
The truth is that gravity "pulls" toward mass regardless of the mass' orientation or configuration.
Thatís incorrect. Gravity pulls in the direction that is determined by the gravitational pull of all the objects around it, the forces adding vectorally. If the particle is in the center of a hollow shell its easy to show that all the masses which make up the shell pull on the particle inside the shell in a way that all the forces acting on it cancel out.

If you donít believe this then right a computer program and have it calculate if for you by arranging a shell of a large number of point particles at equal distance from the origin of the coordinate system. Do you know how to write a computer program. If you donít then do you know someone who does? If so then write the program or have someone write it for you. The math necessary to do this is very simple and requires simple algebra and trigonometry. So little is required that it would only take a few weeks to learn it.

So do it and prove the entire physics community wrong! Youíll win a Nobel Prize in physics. Unless you donít think its worth the effort to actually determine the quantity for yourself?
 

Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #30 on: 28/07/2013 13:56:48 »
Most of the demonstrations of Newton's laws (and Einsteins) have been done from outside a massive object, due to experimental simplicity.

BC's Shell Theorem Link had an interesting note at the bottom, which says that if you could perform the test inside a hollow ball, you may be able to measure something that looks like Einsteins cosmological constant. But the logistics of creating a massive hollow ball far exceeds today's Engineering capabilities!
I disagree. It's easy to create a hollow shell.
For a certain definition of "easy".
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #31 on: 28/07/2013 15:59:14 »
Quote from: Bored chemist
For a certain definition of "easy".
Why is it beyond our engineering capabilities to fabricate a hollow shell of steel one meter thick with a radius of 20 meters? A an engineering feat that's easy by any definition in my humble opinion. It's measuring the gravitational field to high precision that's hard.
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #32 on: 28/07/2013 16:22:28 »
Thibeinn Ė If we seem to come off in a bad way then know that we donít intend to be mean in any way. From what you told us you came here to discuss the gravitational field inside a hollow sphere. We said what we did because we know that there is so much scientific evidenced based on observation that to say that the gravitational field inside a spherical shell of uniform mass density is zero that itís taken as a fact. Itís as much of a fact as the fact that Newtonís Laws and Keplerís laws are accurate to a very high degree of accuracy. Those too are based on observation of the solar system.

When you go some place to argue a point then if there is overwhelming evidence against your belief you can expect an argument against it from those of us who chose to do this as a living. That means we spent many years studying the physics and math and spent many grueling hours working out exercise problems and following well-known proofs of these kinds of things. Weíre not new to this picnic. We are all very skilled as to what can be considered a difference of opinion to a difference in a belief. And this is not something that is subject to opinion. Itís something subject to belief. And we have overwhelming reasons to believe what we do and to recognize the errors in your argument. So this is not a personal thing. Weíre not here to be jerks. Some of us, such as myself, are here to help others understand physics and the math that it requires to understand it fully. To say that thereís a gravitational field inside the sphere is like someone telling a seasoned mechanic that a radiator belt is made of leather and has a buckle. Now thatís not a matter of opinion is it? Have you ever looked under the hood of all cars ever built to make sure the mechanic is right when he tells that person heís wrong? :)
 

Offline Soul Surfer

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Re: How would gravity behave inside a hollow planet?
« Reply #33 on: 28/07/2013 18:43:20 »
Have just caught up with this the fact that the gravitational field inside a uniform hollow shall is zero everywhere is as I said at first very counterintuitive.  Let me try to explain in non mathematical terms

It is easy to see that the force in the centre is zero because in each small solid angle there is exactly the same amount of material at the same distance. 

It is also easy to see that for any point along a radius from the centre, (this is the only possible position any particle can have inside a spherical cavity) because of the symmetry that the forces perpendicular to the radius line are zero because of the symmetry with equal masses at equal distances in all directions.

All that now remains are the forces along the line from the radius from the centre to the edge. Consider now the gravitational forces generated in a point just inside the surface of the hollow sphere. Let us say the shell is "thin" and has a mass of m per unit area.  consider a small solid angle say around a 1 degree cone along the radius line.  Now as the shell is thin if the point is in contact with the inner area the small cone does not include any matter so the force is zero let us now move back a bit say far enough for the cone to intersect 1 unit area of mass m of the shell and that this distance is 1 unit of distance let us now look at the other side of the sphere.   If the distance to the other side is 1 unit we are in the centre and we know that the force is zero.  If it was 2 units of distance the cone would intersect (2 squared) 4 units of area of the shell (the area goes up as the square of the distance) and the gravitational force of the  4 units of mass will be reduced by 1/(2 squared) =  1/4  so the force exactly the same as the 1 unit of mass at 1 unit of length  So a net force of zero this applies whatever the size of the sphere because as the distance goes up and the force is reduced by the inverse square of the distance the mass in the little cone goes up as the square of the distance.

I hope that this is an adequate and simple enough proof.
« Last Edit: 29/07/2013 09:01:17 by Soul Surfer »
 

Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #34 on: 29/07/2013 10:05:42 »
At university, I also saw how Newton's law of gravity could be applied using calculus (also developed by Newton) to show that gravity is uniformly zero throughout a hollow shell.

Up to around the year 1900, it was thought that Newton's law of gravity adequately described the motion of bodies in our solar system. But, guided by Einstein's theory of relativity, we have now detected far more subtle gravitational effects close to the Sun that are better explained by Einstein than by Newton.

We know that Newton's theory becomes very inaccurate in the relativistic vicinity of a black hole. So if you wanted to test the hollow-shell theorem in a relativistic regime, you would pick a neutron star that was just short of becoming a black hole. You would then tunnel out a spherical cavity in the center, and repeat the hollow-shell experiment there.

We know that Newton's theory does not apply on cosmic scales (unlike Einstein's, which had his arbitrary cosmological constant, and today's dark energy theories). To test the hollow-shell theorem in a cosmological context, you would build a hollow-shell structure with the mass of a galactic cluster or more (but without it collapsing into a black hole!).

So while Newton's calculation would give you an answer that is extremely accurate on the scale of a hollow Earth, that does not necessarily extend to relativistic or cosmological environments.
 

Offline Soul Surfer

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Re: How would gravity behave inside a hollow planet?
« Reply #35 on: 29/07/2013 13:44:51 »
Of course not!  But that was not the question.  This deals with a hollow planet.
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #36 on: 29/07/2013 16:14:15 »
Quote from: evan_au
Up to around the year 1900, it was thought that Newton's law of gravity adequately described the motion of bodies in our solar system. But, guided by Einstein's theory of relativity, we have now detected far more subtle gravitational effects close to the Sun that are better explained by Einstein than by Newton.
On that point I derived and expression for the inertial force on a particle in a gravitational field in a Schwarzschild spacetime (spacetime around a spherically symmetric distribution of matter in empty spacetime (i.e. matter is confined within a spherical region). The resulting force is velocity dependant as are all forces in relativity. If the body is falling radially inward or moving tangentially the force is the same and is given here

http://home.comcast.net/~peter.m.brown/gr/force_falling_particle.htm

I also derived this for the tangentially moving body and the result is the same. The result is

Gr = GMm(1 + v2/2)/r2

I find it delightful that here m is relativistic mass defined as m = P[sup0[/sup]/c = time component of 4-momentum (which is not always energy contary to popular belief). :)
 

Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #37 on: 29/07/2013 19:48:23 »
Quote from: Bored chemist
For a certain definition of "easy".
Why is it beyond our engineering capabilities to fabricate a hollow shell of steel one meter thick with a radius of 20 meters? A an engineering feat that's easy by any definition in my humble opinion. It's measuring the gravitational field to high precision that's hard.

You seem to have forgotten what was originally written.
"I disagree. It's easy to create a hollow shell. Just get a small asterod and make it spherical and then hollow it out."
Which is odd, because you wrote it.
It would be fairly easy to make a steel sphere a foot across- they do it all the time.
A few tens of feet isn't a problem.
http://upload.wikimedia.org/wikipedia/commons/6/68/MiRO4.jpg

But none of those matter because it wouldn't be possible to measure the effect of the shell (especially when you are trying to prove that it isn't exactly zero).
You would need to reduce the effect of Earth's gravity for a start- so you would need to put it in orbit.

Are you beginning to see why this isn't actually "easy"?
 

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Re: How would gravity behave inside a hollow planet?
« Reply #38 on: 29/07/2013 23:42:39 »
Quote from: Bored chemist
You seem to have forgotten what was originally written.
Whoops! Sorry my friend. :)
Quote from: Bored chemist
But none of those matter because it wouldn't be possible to measure the effect of the shell (especially when you are trying to prove that it isn't exactly zero).
You would need to reduce the effect of Earth's gravity for a start- so you would need to put it in orbit.
I had in mind the principle of superposition. The gravitational field in a region of space will remain unchanged when surrounded by a spherical shell. The gravitational field of the shell will have no effect on that field. This is one way to check the shell theorem if you first accept the principle of superposition.
Quote from: Bored chemist
Are you beginning to see why this isn't actually "easy"?
Nope. :)

I'm beginning to see how poorly I explained myself though. Does that count? LOL!!
 

Offline Bored chemist

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Re: How would gravity behave inside a hollow planet?
« Reply #39 on: 30/07/2013 20:58:51 »
It's tricky to speculate on how to measure something that we suspect doesn't exist.
Let's work out how easy it is to measure the effect of gravity directly- not the effect of surrounding a "meter" by a shell, but putting a big lump of mass above the "meter" and seeing how much difference it makes.
OK, a decent laboratory balance will resolve changes in weight of the order of a part in 100 million.
You can do a lot better with a gravimeter- but I'm not sure that counts as "easy": we can come back to it.

Now, I propose to put a big lump of stuff above the balance and see if I can measure the change in apparent weight.
How big a lump of stuff do I need?
Well, lets make a simple assumption- I will use "stuff" with about the same density as the Earth.

I will make the blob spherical- again, because it makes the maths easier.
Now, I can put the lump above the balance- the closest I can get it is the radius of the lump.
At that point it will attract the test object on the balance with a force which is proportional to the mass of the lump and inversely proportional to the distance from the centre of the lump.
The same applies to the gravitational attraction of the earth.
So if the lump of stuff is x times smaller than the earth then it will have an attraction x^3 times smaller, because it's less massive, but x^2 times bigger because it's nearer.
Overall, it will have an effect x times smaller than the earth.
If I want to spot that, it needs to be more than a hundred millionth of the attraction due to the earth.
So the lump needs to be no smaller than a hundred million times smaller than the earth.
The radius of the earth is roughly 6000000 metres so you need a lump of stuff that's at least 6,000,000 /100,000,000 metres. i.e. 6/100 metres that's only a few inches.

That looks so easy I'm sure I have made an error in the maths.

 

Offline evan_au

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Re: How would gravity behave inside a hollow planet?
« Reply #40 on: 30/07/2013 22:41:16 »
Cavendish used 2" and 12" lead balls to estimate the strength of gravity, G.

But he mounted them in a horizontal plane, so he wasn't measuring small differences in Earth's attraction - but it was still a very tricky measurement.

See http://en.wikipedia.org/wiki/Cavendish_experiment
 

Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #41 on: 14/09/2013 03:14:30 »
Built your hollow sphere to a particular dimension and do a galileo. Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere. This method should apply to any earth bound hollow sphere no matter the size/mass.
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #42 on: 14/09/2013 04:03:45 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.
 

Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #43 on: 14/09/2013 04:26:08 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.

So are you saying objects dropped from the same height under gravitation would fall at different rates?
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #44 on: 14/09/2013 07:34:12 »
Quote from: jeffreyH
Built your hollow sphere to a particular dimension and do a galileo.
It's impractical to do so and since scientists don't question Newton's law of gravity nobody would build it.
Quote from: jeffreyH
Drop one object inside the sphere at the same time as you drop one outside the sphere. If dropped from the same distance they hit the ground at the same time. Proving zero gravity inside the sphere.
That makes no sense. That is not what physics predicts.

So are you saying objects dropped from the same height under gravitation would fall at different rates?
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.
 

Offline jeffreyH

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Re: How would gravity behave inside a hollow planet?
« Reply #45 on: 14/09/2013 18:43:51 »
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.

My argument was to actually prove your point I wasn't arguing against you.
 

Offline Pmb

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Re: How would gravity behave inside a hollow planet?
« Reply #46 on: 14/09/2013 21:02:51 »
The subject of this thread is the question How would gravity behave inside a hollow planet?
which has been answered several times. There is no gravitational field inside a hollow planet. Therefore an object dropped from inside would move in the exact same way as if there was no planet at all, i.e. it wouldn't drop.

This has been explained over and over. Repeating and arguing about it will not change the answer. This is well known problem in gravitational physics and the answer is well known as well. The solution is calculated fairly easily. There is no mystery here. If you disagree with it then the problem lies in your education of physics, not the physics.

My argument was to actually prove your point I wasn't arguing against you.
Oh. Okay. I actually only try to argue the point where the physics leads me. It's safer than way. :)
 

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Re: How would gravity behave inside a hollow planet?
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